Numerical Simulation of a Thin Heated Layer Separation under Interaction with a Shock Wave

Belotserkovskii, O.M.; Gordeichik, B.N.; Zabavin, V.N.; Scherbin, M.D.

Авторы: Belotserkovskii O.M., Gordeichik B.N., Zabavin V.N., Scherbin M.D.
Сборник: The third Russian-Japan joint symposium on computational fluid dynamics. Book of abstracts. Russia, Vladivostok, August 25-30, 1992
Том: 1
Тезисы
Год издания: 1992
Место издания: DALNAUKA VLADIVOSTOK
Первая страница: 63
Последняя страница: 64
Аннотация: Let us take a nonviscous flow with a shock wave moving along a smooth surface to which a heated layer of gas is adjoined. It is well known that a stationary flow with curved front is formed in case the layer temperature is not too high and it can penetrate into a region behind a shook front. If the layer temperature exceeds some threshold value the global alteration of the whole flow takes place: a precursor is formed in front of an initial shock wave, a vortex separating the heated layer from the surface is formed in the area of interaction, and the flow turns into a non-stationary one. Some results of numerical simulation in such a mode are shown in Fig. 1, In the course of time disturbance made by the heated layer involves an increasingly large portion of space. The solution approaches a semi-similar one in which the heated layer depth becomes quite insignificant in comparison with a charac¬teristic size of disturbance. In practical tasks size of disturbance may exceed the layer depth by two or three orders. It is impossible to use direct numerical simulation for tasks of this type due to limited computer resources. Boundary conditions for numerical simulation of flows with a thin heated layer separation are presented in this study. The depth of the layer here is supposed to be small in comparison with the size of one cell. Preliminary analysis of Euler equations shows that thin heated layer cannot change the general balance of mass, impulse and energy in the flow but it alters the circulation rate variation which is an integral flow characteristic. And the alteration in its first approximation does not depend upon the layer depth but is determined by layer temperature and shock characteristics. To put it in another way the heated layer alters circulation flow in the boundary and brings a+++bout global reformation of the flow. Quality analysis of vorticity formation and transport in the area of shook and heated layer interaction allowed to describe the separation process in the following way. When a shock moves along a layer vortex formation takes place. The mode of interaction may be stationary when all generated vorticity is taken down by the flow away from the interaction region. Yet the rate of circulation taking away may not exceed a certain value depending upon shock parameters while circulation generation rate may increase unlimitedly when heated layer density decreases. Therefore if layer density is less than some threshold value the produced vorticity cannot be taken away out of the interaction region. As a result a growing vortex is formed which evokes layer separation and a precursor wave generation. The above interpretation allowed to produce boundary conditions imitating an infinitely thin heated layer near the surface. We assume that boundary conditions for variables of the Euler equations arc not fulfilled strictly but allow some deviation. The deviation itself is chosen so as to alter circulation flow on the boundary by the value brought about by a heated layer presence, while the layer itself as an area of abated density IS not present in the initial/boundary conditions. This is the way to avoid thin heated layer simulation in the analyzed region and the inner mechanism of interaction — vortex formation being intact. Fig.2 shows some results of numerical simulation of a self-similar task on an infinitely thin heated layer separation. Comparison with the corresponding fields in Fig.1 shows that in the new variant of calculation all principle flow elements are intact but the heated layer itself. A layer of finite depth and the volume it gets into after its separation from the surface can be seen in the density field and by marker from previous calculations. There is no heated layer itself in the density field of the new calculation but one can see a contact boundary line between a backward flow area and a gas flow in the precursor behind the oblique shook front. The contact boundary line should be identified with a thin layer separated from the surface. Both resemblance in quality of the computed data and its numerical agreement should be taken into consideration: circulation in flows, pressure in precursors, shocks front angles of incidence and so on all of them agree quite well. The physical analysis of the task allowed to clear out interaction mechanism between a shook front and a thin heated layer and to produce a method of numerical simulation of this phenomenon.
Добавил в систему: Гордейчик Борис Николаевич

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